The Investigation and Study of Hydrogen Atom in Spherical Cavity Using B-Spline Basis Functions: A Mathematical Approach

ABSTRACT

The following article has been retracted due to the investigation of complaints received against it. The Editorial Board found that substantial portions of the text came from other published papers. The scientific community takes a very strong view on this matter, and the Health treats all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No. 4, 334-339, 2012, has been removed from this site.

The following article has been retracted due to the investigation of complaints received against it. The Editorial Board found that substantial portions of the text came from other published papers. The scientific community takes a very strong view on this matter, and the Health treats all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No. 4, 334-339, 2012, has been removed from this site.

Cite this paper

nullA. Heidari, F. Jahromi, R. Amiri and M. Ghorbani, "The Investigation and Study of Hydrogen Atom in Spherical Cavity Using B-Spline Basis Functions: A Mathematical Approach,"*Journal of Modern Physics*, Vol. 3 No. 4, 2012, pp. 334-339. doi: 10.4236/jmp.2012.34045.

nullA. Heidari, F. Jahromi, R. Amiri and M. Ghorbani, "The Investigation and Study of Hydrogen Atom in Spherical Cavity Using B-Spline Basis Functions: A Mathematical Approach,"

References

[1] V. K. Dolmatov, A. S. Baltenkov, J.-P. Connerade and S. T. Manson, “Structure and Photoionization of Confined Atoms,” Radiation Physics and Chemistry, Vol. 70, No. 1-3, 2004, pp. 417-433. doi:10.1016/j.radphyschem.2003.12.024

[2] A. Michels, J. Deboer and A. Bijl, “Remarks Concerning Molecural Interaction and Their Influence on the Polarisability,” Physica, Vol. 4, 1937, pp. 981-994. doi:10.1016/S0031-8914(37)80196-2

[3] S. Kang, Q. Liu, H. Y. Meng and T. Y. Shi, “Hydrogen Atom in Ellipsoidal Cavity,” Physics Letters A, Vol. 360, No. 4-5, 2007, pp. 608-614. doi:10.1016/j.physleta.2006.08.055

[4] S. H. Patil, “Hydrogen Atom Confined to an Ellipsoid,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 34, No. 6, 2001, p. 1049. doi:10.1088/0953-4075/34/6/306

[5] T. Guillot, “A Comparison of the Interiors of Jupiter and Saturn,” Planetary and Space Science, Vol. 47, No. 10-11, 1999, pp. 1183-11200. doi:10.1016/S0032-0633(99)00043-4

[6] T. Y. Shi, H. X. Qiao and B. W. Li, “Variational Calculations for a Hydrogen Atom Confined Off-Centre in an Impenetrable Spherical Box Using B-Splines,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 33, No. 9, 2000, p. L349. doi:10.1088/0953-4075/33/9/106

[7] H. Bachau, E. Cormier, P. Decleva, J. E. Hansen and F. Martín, “Applications of B-Splines in Atomic and Molecular Physics,” Reports on Progress in Physics, Vol. 64, No. 12, 2001, p. 1815. doi:10.1088/00344885/64/12/205.

[8] W. R. Johnson and J. Sapirstein, “Computation of Second-Order Many-Body Corrections in Relativistic Atomic Systems,” Physical Review Letters, Vol. 57, No. 9, 1986, pp. 1126-1129. doi:10.1103/PhysRevLett.57.1126

[9] D. A. Horner, S. Miyabe, T. N. Rescigno, C. W. McCurdy, F. Morales and F. Martín, “Classical Two-Slit Interference Effects in Double Photoionization of Molecular Hydrogen at High Energies,” Physical Review Letters, Vol. 101, No. 18, 2008, pp. 183002-183005. doi:10.1103/PhysRevLett.101.183002

[10] D. A. Horner, C. W. McCurdy and T. N. Rescigno, “Triple Differential Cross Sections and Nuclear Recoil in Two-Photon Double Ionization of Helium,” Physical Review A, Vol. 78, No. 4, 2008, Article ID 04341. doi:10.1103/PhysRevA.78.043416

[11] A. Palacios, T. N. Rescigno and C. W. McCurdy, “Cross Sections for Short-Pulse Single and Double Ionization of Helium,” Physical Review A, Vol. 77, No. 3, 2008, Article ID 032716.

[12] F. L. Yip, C. W. McCurdy and T. N. Rescigno, “Hybrid Gaussian-Discrete-Variable Representation Approach to Molecular Continuum Processes: Application to Photoionization of Diatomic Li2+,” Physical Review A, Vol. 78, No. 2, 2008, Article ID 023405. doi:10.1103/PhysRevA.78.023405

[13] P. L. Bartlett, A. T. Stelbovics, T. N. Rescigno and C. W. McCurdy, “Application of Exterior Complex Scaling to Positron-Hydrogen Collisions including Rearrangement,” Physical Review A, Vol. 77, No. 3, 2008, Article ID 032710. doi:10.1103/PhysRevA.77.032710

[14] D. A. Horner, W. Vanroose, T. N. Rescigno, F. Martin and C. W. McCurdy, “The Role of Nuclear Motion in the Photo-Double Ionization of Molecular Hydrogen,” Lawrence Berkeley National Laboratory, Paper LBNL-61189, 2008.

[15] J. C. Morrison and C. Bottcher, “Spline Collocation Methods for Calculating Orbital Energies,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 26, No. 22, 1993, pp. 3999-4006. doi:10.1088/0953-4075/26/22/007.

[16] W. R. Johnson, S. A. Blundell and J. Sapirstein, “Finite Basis Sets for the Dirac Equation Constructed from B Splines,” Physical Review A, Vol. 37, No. 2, 1988, pp. 307-315. doi:10.1103/PhysRevA.37.307

[17] W. R. Johnson, S. A. Blundell and J. Sapirstein, “Many-Body Perturbation-Theory Calculations of Energy Levels along the Lithium Isoelectronic Sequence,” Physical Review A, Vol. 37, No. 8, 1988, pp. 2764-2777. doi:10.1103/PhysRevA.37.2764

[18] W. R. Johnson, S. A. Blundell and J. Sapirstein, “Many-Body Perturbation-Theory Calculations of Energy Levels along the Sodium Isoelectronic Sequence,” Physical Re- view A, Vol. 38, No. 6, 1988, pp. 2699-2706. doi:10.1103/PhysRevA.38.2699

[19] W. R. Johnson, S. A. Blundell, Z. W. Liu and J. Sapirstein, “Correlation Effects in the Parity-Noncomserving 6s→7s Transition in Cesium,” Physical Review A, Vol. 37, 1988, pp. 1395-1400. doi:10.1103/PhysRevA.37.1395

[20] S. A. Blundell, W. R. Johnson and J. Sapirstein, “Higher-Order Many-Body Perturbation-Theory Calculations of Energy Levels in Cesium,” Physical Review A, Vol. 38, No. 10, 1988, pp. 4961-4966. doi:10.1103/PhysRevA.38.4961

[21] T. K. Fang and T. N. Chang, “Photoionization from Excited Mg Atoms,” Physical Review A, Vol. 61, No. 5, 2000, Article ID 052716. doi:10.1103/PhysRevA.61.052716

[22] T. K. Fang and T. N. Chang, “B-Spline-Based Multichan-Nel K-Matrix Method for Atomic Photoionization,” Physical Review A, Vol. 61, No. 6, 2000, Article ID 062704. doi:10.1103/PhysRevA.61.062704

[23] C. W. McCurdy and F. Martin, “Implementation of Exterior Complex Scaling in B-Splines to Solve Atomic and Molecular Collision Problems,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 37, No. 4, 2004, p. 917. doi:10.1088/0953-4075/37/4/017

[24] B. Nine, O. Haif-Khaif and A. Zerarka, “The Eigenenergies of the Wave Function through the Non-Variational Galerkin-B-Spline Approach,” Applied Mathematics and Computation, Vol. 178, No. 2, 2006, pp. 486-492. doi:10.1016/j.amc.2005.11.067

[25] N. Aquino, G. Campoy and H. E. Montgomery Jr., “Highly Accurate Solutions for the Confined Hydrogen Atom,” International Journal of Quantum Chemistry, Vol. 107, No. 7, 2007, pp. 1548-1558. doi:10.1002/qua.21313

[26] S. Goldman and C. Joslin, “Spectroscopic Properties of an Isotropically Compressed Hydrogen Atom,” Journal of Physical Chemistry, Vol. 96, No. 14, 1992, pp. 6021-6027. doi:10.1021/j100193a069

[1] V. K. Dolmatov, A. S. Baltenkov, J.-P. Connerade and S. T. Manson, “Structure and Photoionization of Confined Atoms,” Radiation Physics and Chemistry, Vol. 70, No. 1-3, 2004, pp. 417-433. doi:10.1016/j.radphyschem.2003.12.024

[2] A. Michels, J. Deboer and A. Bijl, “Remarks Concerning Molecural Interaction and Their Influence on the Polarisability,” Physica, Vol. 4, 1937, pp. 981-994. doi:10.1016/S0031-8914(37)80196-2

[3] S. Kang, Q. Liu, H. Y. Meng and T. Y. Shi, “Hydrogen Atom in Ellipsoidal Cavity,” Physics Letters A, Vol. 360, No. 4-5, 2007, pp. 608-614. doi:10.1016/j.physleta.2006.08.055

[4] S. H. Patil, “Hydrogen Atom Confined to an Ellipsoid,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 34, No. 6, 2001, p. 1049. doi:10.1088/0953-4075/34/6/306

[5] T. Guillot, “A Comparison of the Interiors of Jupiter and Saturn,” Planetary and Space Science, Vol. 47, No. 10-11, 1999, pp. 1183-11200. doi:10.1016/S0032-0633(99)00043-4

[6] T. Y. Shi, H. X. Qiao and B. W. Li, “Variational Calculations for a Hydrogen Atom Confined Off-Centre in an Impenetrable Spherical Box Using B-Splines,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 33, No. 9, 2000, p. L349. doi:10.1088/0953-4075/33/9/106

[7] H. Bachau, E. Cormier, P. Decleva, J. E. Hansen and F. Martín, “Applications of B-Splines in Atomic and Molecular Physics,” Reports on Progress in Physics, Vol. 64, No. 12, 2001, p. 1815. doi:10.1088/00344885/64/12/205.

[8] W. R. Johnson and J. Sapirstein, “Computation of Second-Order Many-Body Corrections in Relativistic Atomic Systems,” Physical Review Letters, Vol. 57, No. 9, 1986, pp. 1126-1129. doi:10.1103/PhysRevLett.57.1126

[9] D. A. Horner, S. Miyabe, T. N. Rescigno, C. W. McCurdy, F. Morales and F. Martín, “Classical Two-Slit Interference Effects in Double Photoionization of Molecular Hydrogen at High Energies,” Physical Review Letters, Vol. 101, No. 18, 2008, pp. 183002-183005. doi:10.1103/PhysRevLett.101.183002

[10] D. A. Horner, C. W. McCurdy and T. N. Rescigno, “Triple Differential Cross Sections and Nuclear Recoil in Two-Photon Double Ionization of Helium,” Physical Review A, Vol. 78, No. 4, 2008, Article ID 04341. doi:10.1103/PhysRevA.78.043416

[11] A. Palacios, T. N. Rescigno and C. W. McCurdy, “Cross Sections for Short-Pulse Single and Double Ionization of Helium,” Physical Review A, Vol. 77, No. 3, 2008, Article ID 032716.

[12] F. L. Yip, C. W. McCurdy and T. N. Rescigno, “Hybrid Gaussian-Discrete-Variable Representation Approach to Molecular Continuum Processes: Application to Photoionization of Diatomic Li2+,” Physical Review A, Vol. 78, No. 2, 2008, Article ID 023405. doi:10.1103/PhysRevA.78.023405

[13] P. L. Bartlett, A. T. Stelbovics, T. N. Rescigno and C. W. McCurdy, “Application of Exterior Complex Scaling to Positron-Hydrogen Collisions including Rearrangement,” Physical Review A, Vol. 77, No. 3, 2008, Article ID 032710. doi:10.1103/PhysRevA.77.032710

[14] D. A. Horner, W. Vanroose, T. N. Rescigno, F. Martin and C. W. McCurdy, “The Role of Nuclear Motion in the Photo-Double Ionization of Molecular Hydrogen,” Lawrence Berkeley National Laboratory, Paper LBNL-61189, 2008.

[15] J. C. Morrison and C. Bottcher, “Spline Collocation Methods for Calculating Orbital Energies,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 26, No. 22, 1993, pp. 3999-4006. doi:10.1088/0953-4075/26/22/007.

[16] W. R. Johnson, S. A. Blundell and J. Sapirstein, “Finite Basis Sets for the Dirac Equation Constructed from B Splines,” Physical Review A, Vol. 37, No. 2, 1988, pp. 307-315. doi:10.1103/PhysRevA.37.307

[17] W. R. Johnson, S. A. Blundell and J. Sapirstein, “Many-Body Perturbation-Theory Calculations of Energy Levels along the Lithium Isoelectronic Sequence,” Physical Review A, Vol. 37, No. 8, 1988, pp. 2764-2777. doi:10.1103/PhysRevA.37.2764

[18] W. R. Johnson, S. A. Blundell and J. Sapirstein, “Many-Body Perturbation-Theory Calculations of Energy Levels along the Sodium Isoelectronic Sequence,” Physical Re- view A, Vol. 38, No. 6, 1988, pp. 2699-2706. doi:10.1103/PhysRevA.38.2699

[19] W. R. Johnson, S. A. Blundell, Z. W. Liu and J. Sapirstein, “Correlation Effects in the Parity-Noncomserving 6s→7s Transition in Cesium,” Physical Review A, Vol. 37, 1988, pp. 1395-1400. doi:10.1103/PhysRevA.37.1395

[20] S. A. Blundell, W. R. Johnson and J. Sapirstein, “Higher-Order Many-Body Perturbation-Theory Calculations of Energy Levels in Cesium,” Physical Review A, Vol. 38, No. 10, 1988, pp. 4961-4966. doi:10.1103/PhysRevA.38.4961

[21] T. K. Fang and T. N. Chang, “Photoionization from Excited Mg Atoms,” Physical Review A, Vol. 61, No. 5, 2000, Article ID 052716. doi:10.1103/PhysRevA.61.052716

[22] T. K. Fang and T. N. Chang, “B-Spline-Based Multichan-Nel K-Matrix Method for Atomic Photoionization,” Physical Review A, Vol. 61, No. 6, 2000, Article ID 062704. doi:10.1103/PhysRevA.61.062704

[23] C. W. McCurdy and F. Martin, “Implementation of Exterior Complex Scaling in B-Splines to Solve Atomic and Molecular Collision Problems,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 37, No. 4, 2004, p. 917. doi:10.1088/0953-4075/37/4/017

[24] B. Nine, O. Haif-Khaif and A. Zerarka, “The Eigenenergies of the Wave Function through the Non-Variational Galerkin-B-Spline Approach,” Applied Mathematics and Computation, Vol. 178, No. 2, 2006, pp. 486-492. doi:10.1016/j.amc.2005.11.067

[25] N. Aquino, G. Campoy and H. E. Montgomery Jr., “Highly Accurate Solutions for the Confined Hydrogen Atom,” International Journal of Quantum Chemistry, Vol. 107, No. 7, 2007, pp. 1548-1558. doi:10.1002/qua.21313

[26] S. Goldman and C. Joslin, “Spectroscopic Properties of an Isotropically Compressed Hydrogen Atom,” Journal of Physical Chemistry, Vol. 96, No. 14, 1992, pp. 6021-6027. doi:10.1021/j100193a069